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PubMed1998

A comparison of 180 degrees and 360 degrees acquisition for attenuation-compensated thallium-201 SPECT images.

UNLABELLED: This study compared attenuation compensated, myocardial SPECT images reconstructed from 180 degrees and 360 degrees data to determine if either data acquisition method might yield improved image quality. Specifically, this study analyzed how the use of either 180 degrees or 360 degrees data affects: (a) the relative count density distribution, (b) defect contrast and (c) level of statistical noise in the left ventricular (LV) wall in the reconstructed SPECT images. METHODS: Using the three-dimensional MCAT phantom simulating 201Tl uptake in the upper torso and the SIMSET Monte Carlo code, noise-free projection datasets for both 180 degrees (45 degrees LPO to 45 degrees RAO) and 360 degrees acquisition were generated with the effects of nonuniform attenuation, collimator-detector response and scatter. In addition, low-noise experimental phantom data were acquired over 180 degrees and 360 degrees. Assuming the same total acquisition time, four sets of noisy projection data were simulated from scaled noise-free, simulated data for the following acquisitions: (a) 180 degrees and (b) 360 degrees data acquired on a 90 degrees dual-detector system and (c) 180 degrees and (d) 360 degrees data acquired on a 120 degrees triple-detector system. For each of the four acquisition schemes, 400 realizations of noisy projection data were generated, and the normalized s.d. in the reconstructed images was calculated for five ROIs in the LV wall. Images were reconstructed with nonuniform attenuation compensation using ML-EM algorithm for 25, 50 and 75 iterations. RESULTS: Both the simulated noise-free and experimental low-noise images reconstructed from 180 degrees and 360 degrees data showed nearly identical count densities and defect contrasts in the LV wall. For the 90 degrees dual-detector system, 180 degrees images showed less noise, while for the 120 degrees triple-detector system, 360 degrees showed less noise; however, these differences in noise level were extremely small after a smoothing filter was applied. The 180 degrees images acquired with the 90 degrees dual-detector system showed the same noise level as the 360 degrees images acquired with the 120 degrees triple-detector system, so neither system geometry had an advantage with respect to reduced noise in the SPECT images. CONCLUSION: When nonuniform attenuation compensation is included in the reconstruction, the count density in the LV wall is nearly identical for 180 degrees and 360 degrees SPECT images, and the 90 degrees dual-detector and 120 degrees triple-detector SPECT systems produced similar SPECT images for the same total acquisition time.

Algorithms↗

PubMed1998

Automatic record hash coding and linkage for epidemiological follow-up data confidentiality.

A protocol is proposed to allow linkage of anonymous medical information within the framework of epidemiological follow-up studies. The protocol is composed of two steps; the first concerns the irreversible transformation of identification data, using a one-way hash function which is used after spelling processing. To avoid dictionary attacks, two large random files of keys, called pads, are introduced. The second step consists in the linkage of files rendered anonymous. The weight given to each linkage field is estimated by a mixture model, the likelihood of which being maximized with the Expectation and Maximization (EM) algorithm. The performance of this method has been assessed by comparing record linkage, based on exclusive use of the automatic procedure, with a manual linkage, obtained by the Burgundy Registry of Digestive Cancers. The result of the linkage of a file of 2,847 cancers with a file of 388,614 hospitalization stays in the Dijon university hospital showed a sensitivity of 97% and a specificity of 93%.

Algorithms↗

PubMed1997

Expectation maximization reconstruction of positron emission tomography images using anatomical magnetic resonance information.

Using statistical methods the reconstruction of positron emission tomography (PET) images can be improved by high-resolution anatomical information obtained from magnetic resonance (MR) images. We implemented two approaches that utilize MR data for PET reconstruction. The anatomical MR information is modeled as a priori distribution of the PET image and combined with the distribution of the measured PET data to generate the a posteriori function from which the expectation maximization (EM)-type algorithm with a maximum a posteriori (MAP) estimator is derived. One algorithm (Markov-GEM) uses a Gibbs function to model interactions between neighboring pixels within the anatomical regions. The other (Gauss-EM) applies a Gauss function with the same mean for all pixels in a given anatomical region. A basic assumption of these methods is that the radioactivity is homogeneously distributed inside anatomical regions. Simulated and phantom data are investigated under the following aspects: count density, object size, missing anatomical information, and misregistration of the anatomical information. Compared with the maximum likelihood-expectation maximization (ML-EM) algorithm the results of both algorithms show a large reduction of noise with a better delineation of borders. Of the two algorithms tested, the Gauss-EM method is superior in noise reduction (up to 50%). Regarding incorrect a priori information the Gauss-EM algorithm is very sensitive, whereas the Markov-GEM algorithm proved to be stable with a small change of recovery coefficients between 0.5 and 3%.

Algorithms↗

PubMed1995

An analytical approach for compensation of non-uniform attenuation in cardiac SPECT imaging.

Photon attenuation can reduce the diagnostic accuracy of cardiac SPECT imaging. Bellini et al have previously derived a mathematically exact method to compensate for attenuation in a uniform attenuator. Since the human thorax contains structures with differing attenuation properties, non-uniform attenuation compensation is required in cardiac SPECT. Given an estimate of the patient attenuation map, we show that the Bellini attenuation compensation method can be used in cardiac SPECT to provide a quantitatively accurate reconstruction of a central region in the image which includes the heart and surrounding soft tissue. Simulations using a mathematical cardiac-torso phantom were conducted to evaluate the Bellini method and to compare its performance to the ML-EM iterative algorithm, and to 180 degrees and 360 degrees filtered backprojection (FBP) with no attenuation compensation. 'Bulls-eye' polar maps and circumferential profiles showed that both the Bellini method and the ML-EM algorithm provided quantitatively accurate reconstructions of the myocardium, with a substantial reduction in attenuation-induced artifacts that were observed in the FBP images. The computational load required to implement the Bellini method is approximately equivalent to that required for one iteration of the ML-EM algorithm, thus it is suitable for routine clinical use.

Algorithms↗

PubMed2003

Quantitative comparison of FBP, EM, and Bayesian reconstruction algorithms for the IndyPET scanner.

We quantitatively compare filtered backprojection (FBP), expectation-maximization (EM), and Bayesian reconstruction algorithms as applied to the IndyPET scanner--a dedicated research scanner which has been developed for small and intermediate field of view imaging applications. In contrast to previous approaches that rely on Monte Carlo simulations, a key feature of our investigation is the use of an empirical system kernel determined from scans of line source phantoms. This kernel is incorporated into the forward model of the EM and Bayesian algorithms to achieve resolution recovery. Three data sets are used, data collected on the IndyPET scanner using a bar phantom and a Hoffman three-dimensional brain phantom, and simulated data containing a hot lesion added to a uniform background. Reconstruction quality is analyzed quantitatively in terms of bias-variance measures (bar phantom) and mean square error (lesion phantom). We observe that without use of the empirical system kernel, the FBP, EM, and Bayesian algorithms give similar performance. However, with the inclusion of the empirical kernel, the iterative algorithms provide superior reconstructions compared with FBP, both in terms of visual quality and quantitative measures. Furthermore, Bayesian methods outperform EM. We conclude that significant improvements in reconstruction quality can be realized by combining accurate models of the system response with Bayesian reconstruction algorithms.

Algorithms↗

PubMed2001

Model-based estimation of ultrasonic echoes. Part I: analysis and algorithms.

The patterns of ultrasonic backscattered echoes represent valuable information pertaining to the geometric shape, size, and orientation of the reflectors as well as the microstructure of the propagation path. Accurate estimation of the ultrasonic echo pattern is essential in determining the object/propagation path properties. In this study, we model ultrasonic backscattered echoes in terms of superimposed Gaussian echoes corrupted by noise. Each Gaussian echo in the model is a nonlinear function of a set of parameters: echo bandwidth, arrival time, center frequency, amplitude, and phase. These parameters are sensitive to the echo shape and can be linked to the physical properties of reflectors and frequency characteristics of the propagation path. We address the estimation of these parameters using the maximum likelihood estimation (MLE) principle, assuming that all of the parameters describing the shape of the echo are unknown but deterministic. In cases for which noise is characterized as white Gaussian, the MLE problem simplifies to a least squares (LS) estimation problem. The iterative LS optimization algorithms when applied to superimposed echoes suffer from the problem of convergence and exponential growth in computation as the number of echoes increases. In this investigation, we have developed expectation maximization (EM)-based algorithms to estimate ultrasonic signals in terms of Gaussian echoes. The EM algorithms translate the complicated superimposed echoes estimation into isolated echo estimations, providing computational versatility. The algorithm outperforms the LS methods in terms of independence to the initial guess and convergence to the optimal solution, and it resolves closely spaced overlapping echoes.

Journal Article↗

PubMed1991

Quantitative SPECT reconstruction of iodine-123 data.

Many clinical and research studies in nuclear medicine require quantitation of iodine-123 (123I) distribution for the determination of kinetics or localization. The objective of this study was to implement several reconstruction methods designed for single-photon emission computed tomography (SPECT) using 123I and to evaluate their performance in terms of quantitative accuracy, image artifacts, and noise. The methods consisted of four attenuation and scatter compensation schemes incorporated into both the filtered backprojection/Chang (FBP) and maximum likelihood-expectation maximization (ML-EM) reconstruction algorithms. The methods were evaluated on data acquired of a phantom containing a hot sphere of 123I activity in a lower level background 123I distribution and nonuniform density media. For both reconstruction algorithms, nonuniform attenuation compensation combined with either scatter subtraction or Metz filtering produced images that were quantitatively accurate to within 15% of the true value. The ML-EM algorithm demonstrated quantitative accuracy comparable to FBP and smaller relative noise magnitude for all compensation schemes.

Humans↗

PubMed1989

Estimation of parameters and missing values under a regression model with non-normally distributed and non-randomly incomplete data.

We carried out a simulation study to compare the performance of three algorithms (complete cases, ALLVALUE, and expectation maximization, EM) in estimating regression parameters and missing values for situations that have varying amounts of missing data, distributions (normal, mixture of normals and lognormal), patterns of incomplete data (random, related and censored), and degrees of correlational structure among the dependent and independent variables. We found that the EM and complete cases algorithms performed equally well regardless of the correlational structure, when the percentage of incomplete data was only 5 per cent. When this percentage increased to 25 per cent, the EM algorithm was generally best for estimation, but the complete cases algorithm was safe and conservative. This finding may be attributed to the study design, which required that the slopes be the same in the population of all cases, and in the population of complete cases. In addition, the one-step imputing method (ALLVALUE) was competitive only for situations with weak correlational structure and/or little missing data. In that situation the bias caused with use of all available information was less than that caused with use of only complete cases. On the other hand, for imputation, the EM algorithm performed optimally, even in situations of censored or log-normally distributed data.

Algorithms↗

PubMed2006

Deblurring of breathing motion artifacts in thoracic PET images by deconvolution methods.

In FDG-PET imaging of thoracic tumors, blurring due to breathing motion often significantly degrades the quality of the observed image, which then obscures the tumor boundary. We demonstrate a deblurring technique that combines patient-specific motion estimates of tissue trajectories with image deconvolution techniques, thereby partially eliminating breathing-motion induced artifacts. Two data sets were used to evaluate the methodology including mobile phantoms and clinical images. The clinical images consist of PET/CT co-registered images of patients diagnosed with lung cancer. A breathing motion model was used to locally estimate the location-dependent tissue location probability function (TLP) due to breathing. The deconvolution process is carried by an expectation-maximization (EM) iterative algorithm using the motion-based TLP. Several methods were used to improve the robustness of the deblurring process by mitigating noise amplification and compensating for motion estimate uncertainties. The mobile phantom study with controlled settings demonstrated significant reduction in underestimation error of concentration in high activity case without significant superiority between the different applied methods. In case of medium activity concentration (moderate noise levels), less improvement was reported (10%-15% reduction in underestimation error relative to 15%-20% reduction in high concentration). Residual denoising using wavelets offered the best performance for this case. In the clinical data case, the image spatial resolution was significantly improved, especially in the direction of greatest motion (cranio-caudal). The EM algorithm converged within 15 and 5 iterations in the large and small tumor cases, respectively. A compromise between a figure-of-merit and entropy minimization was suggested as a stopping criterion. Regularization techniques such as wavelets and Bayesian methods provided further refinement by suppressing noise amplification. Our initial results show that the proposed method provides a feasible framework for improving PET thoracic images, without the need for gated/4-D PET imaging, when 4-D CT is available to estimate tumor motion.

Algorithms↗

PubMed2004

A method for imputing missing data in longitudinal studies.

PURPOSE: In a cohort in which racial data are unknown for some persons, race-specific persons and person-years are imputed using a model-based iterative allocation algorithm (IAA). METHODS: An EM algorithm-based approach to address misclassification in a censored data regression setting can be adapted to estimate the probability that a person of unknown race is white. The corresponding race-specific person-years are obtained as a by-product of the estimation procedure. Variance estimates are computed using the bootstrap. The proposed approach is compared with the proportional allocation method (PAM). RESULTS: In an occupational cohort where racial data were missing for 41% of the workers, the age-time-race-specific person-years were estimated within a relative variation of approximately 20%, using the IAA. The deaths were less reliably estimated. The standardized mortality ratios (SMRs) for all-cause mortality estimated using the IAA and the PAM were more similar for the non-white workers than for a smaller subgroup of white workers. CONCLUSIONS: The IAA provides a method to reliably estimate race-specific person-year denominators in cohort studies with missing racial data. This method is applicable to other incompletely observed non-time-dependent categorical covariates. Internal cohort rates or SMRs can be computed and modeled, with bootstrap confidence intervals that account for the uncertainty in the determination of race.

Adolescent↗

PubMed1996

A non-negative fast multiplicative algorithm in 3D scatter-compensated SPET reconstruction.

Single-photon emission tomographic (SPET) reconstruction can be improved, especially for noisy images, by using the iterative expectation-maximization of the maximum-likelihood (EM-ML) algorithm. Its application to clinical routine is, however, hampered by the high number of iterations necessary to achieve acceptable results. Therefore various methods have been developed to accelerate the EM-ML algorithm. In this paper a new accelerated EM-ML-like multiplicative algorithm is proposed for SPET reconstruction. Contrary to some other accelerating methods, it preserves two of the most important properties of the EM-ML, namely pixel positivity inside the patient body and null activity outside. The convergence speed is improved by a factor which can reach 100 in high spatial frequency or low count regions. Good estimates in the low count region are obtained without any smoothing, even at typical routine clinical count rates. The algorithm used in conjunction with the 3D effective one scatter path model provides high-quality SPET images and accurate quantitation.

Adult↗

PubMed2006

Genetic analysis of growth curves using the SAEM algorithm.

The analysis of nonlinear function-valued characters is very important in genetic studies, especially for growth traits of agricultural and laboratory species. Inference in nonlinear mixed effects models is, however, quite complex and is usually based on likelihood approximations or Bayesian methods. The aim of this paper was to present an efficient stochastic EM procedure, namely the SAEM algorithm, which is much faster to converge than the classical Monte Carlo EM algorithm and Bayesian estimation procedures, does not require specification of prior distributions and is quite robust to the choice of starting values. The key idea is to recycle the simulated values from one iteration to the next in the EM algorithm, which considerably accelerates the convergence. A simulation study is presented which confirms the advantages of this estimation procedure in the case of a genetic analysis. The SAEM algorithm was applied to real data sets on growth measurements in beef cattle and in chickens. The proposed estimation procedure, as the classical Monte Carlo EM algorithm, provides significance tests on the parameters and likelihood based model comparison criteria to compare the nonlinear models with other longitudinal methods.

Algorithms↗

PubMed1997

A focus-of-attention preprocessing scheme for EM-ML PET reconstruction.

The expectation-maximization maximum-likelihood (EM-ML) algorithm belongs to a family of algorithms that compute positron emission tomography (PET) reconstructions by iteratively solving a large linear system of equations. We describe a preprocessing scheme for automatically focusing the attention, and thus the computational resources, on a subset of the equations and unknowns. Experimental work with a CM-5 parallel computer implementation using a simulated phantom as well as real data obtained from an ECAT 921 PET scanner indicates that quite significant savings can be obtained with respect to both time and space requirements of the EM-ML algorithm without compromising the quality of the reconstructed images.

Abdomen↗

PubMed2001

Fast EM-like methods for maximum "a posteriori" estimates in emission tomography.

The maximum-likelihood (ML) approach in emission tomography provides images with superior noise characteristics compared to conventional filtered backprojection (FBP) algorithms. The expectation-maximization (EM) algorithm is an iterative algorithm for maximizing the Poisson likelihood in emission computed tomography that became very popular for solving the ML problem because of its attractive theoretical and practical properties. Recently, (Browne and DePierro, 1996 and Hudson and Larkin, 1994) block sequential versions of the EM algorithm that take advantage of the scanner's geometry have been proposed in order to accelerate its convergence. In Hudson and Larkin, 1994, the ordered subsets EM (OS-EM) method was applied to the ML problem and a modification (OS-GP) to the maximum a posteriori (MAP) regularized approach without showing convergence. In Browne and DePierro, 1996, we presented a relaxed version of OS-EM (RAMLA) that converges to an ML solution. In this paper, we present an extension of RAMLA for MAP reconstruction. We show that, if the sequence generated by this method converges, then it must converge to the true MAP solution. Experimental evidence of this convergence is also shown. To illustrate this behavior we apply the algorithm to positron emission tomography simulated data comparing its performance to OS-GP.

Algorithms↗

PubMed2004

An algorithm for molecular dissection of tumor progression.

The volumetric growth of tumor cells as a function of time is most often likely to be a complex trait, controlled by the combined influences of multiple genes and environmental influences. Genetic mapping has proven to be a powerful tool for detecting and identifying specific genes affecting complex traits, i.e., quantitative trait loci (QTL), based on polymorphic markers. In this article, we present a novel statistical model for genetic mapping of QTL governing tumor growth trajectories in humans. In principle, this model is a combination of functional mapping proposed to map function-valued traits and linkage disequilibrium mapping designed to provide high resolution mapping of QTL by making use of recombination events created at a historic time. We implement an EM-simplex hybrid algorithm for parameter estimation, in which a closed-form solution for the EM algorithm is derived to estimate the population genetic parameters of QTL including the allele frequencies and the coefficient of linkage disequilibrium, and the simplex algorithm incorporated to estimate the curve parameters describing the dynamic changes of cancer cells for different QTL genotypes. Extensive simulations are performed to investigate the statistical properties of our model. Through a number of hypothesis tests, our model allows for cutting-edge studies aimed to decipher the genetic mechanisms underlying cancer growth, development and differentiation. The implications of our model in gene therapy for cancer research are discussed.

Algorithms↗

PubMed1995

A two-step iterative algorithm for estimation in nonlinear mixed-effect models with an evaluation in population pharmacokinetics.

This article proposes an EM-like algorithm for estimating, by maximum likelihood, the population parameters of a nonlinear mixed-effect model given sparse individual data. The first step involves Bayesian estimation of the individual parameters. During the second step, population parameters are estimated using a linearization about those Bayesian estimates. This algorithm (implemented in P-PHARM) is evaluated on simulated data, mimicking pharmacokinetic analyses and compared to the First-Order method and the First-Order Conditional Estimates method (both implemented in NONMEM). The accuracy of the results, within few iterations, shows the estimation capabilities of the proposed approach.

Algorithms↗

PubMed2026

A flexible framework for robust and efficient Mendelian randomization with debiasing.

Mendelian randomization (MR) has been widely used to infer causal relationships between exposures and outcomes in epidemiological studies. However, classical MR assumptions can be violated when genetic variants are associated with outcomes through pathways other than the exposure, leading to uncorrelated and/or correlated pleiotropy. Additionally, measurement error arising from the inherent uncertainty in summary statistics obtained from large-scale genome-wide association studies can introduce bias into the causal effect estimate. To address these issues, we develop a debiased mixture inverse variance weighting ($\mathsf{dmIVW}$) method with three major advantages. First, it is capable of simultaneously handling various types of pleiotropy and eliminating the bias caused by uncertainty. Second, it can guard against distortion caused by invalid genetic variants while effectively harnessing their information. Third, our unified framework facilitates a fair comparison and combination of a series of submodels, encompassing several popular MR methods as special cases. Through real data applications, the effectiveness and robustness of $\mathsf{dmIVW}$ in estimating the causal effects of risk factors on common diseases are demonstrated.

Mendelian Randomization Analysis↗

PubMed2005

Noise characterization of block-iterative reconstruction algorithms: II. Monte Carlo simulations.

In Soares et al. (2000), the ensemble statistical properties of the rescaled block-iterative expectation-maximization (RBI-EM) reconstruction algorithm and rescaled block-iterative simultaneous multiplicative algebraic reconstruction technique (RBI-SMART) were derived. Included in this analysis were the special cases of RBI-EM, maximum-likelihood EM (ML-EM) and ordered-subset EM (OS-EM), and the special case of RBI-SMART, SMART. Explicit expressions were found for the ensemble mean, covariance matrix, and probability density function of RBI reconstructed images, as a function of iteration number. The theoretical formulations relied on one approximation, namely that the noise in the reconstructed image was small compared to the mean image. In this paper, we evaluate the predictions of the theory by using Monte Carlo methods to calculate the sample statistical properties of each algorithm and then compare the results with the theoretical formulations. In addition, the validity of the approximation will be justified.

Algorithms↗